The position of a particle moving along the x-axis is given by
x = (13 + 11t − 1.5t2), where t is in seconds and x is in meters. What is the average velocity during the time interval from t = 1s to t = 4 s?
v = -3 t + 11
since v linear in t, find at t = 1 and at t = 4 and average
or alternatively
at t = 4
x = 13 + 44 - 24 = 33
at t = 1
x = 13 + 11 - 1.5 = 22.5
33-22.5 = 10.5 meters moved in 3 seconds
so average = 10.5/3 = 3.5 meters/second
or
find v at 2.5 = t = (1+4)/2
v = 11-3 t = 3.5 meters/s again :)
To find the average velocity during the time interval from t = 1s to t = 4s, we need to calculate the change in position (Δx) and change in time (Δt) during this interval.
Given:
x = 13 + 11t - 1.5t^2,
we can find the position at t = 1s and t = 4s:
At t = 1s, substituting t = 1 into the equation, we get:
x1 = 13 + 11(1) - 1.5(1^2) = 22.5.
At t = 4s, substituting t = 4 into the equation, we get:
x2 = 13 + 11(4) - 1.5(4^2) = -15.
Now, we can calculate the change in position (Δx) and change in time (Δt):
Δx = x2 - x1 = (-15) - (22.5) = -37.5 meters.
Δt = t2 - t1 = 4 - 1 = 3 seconds.
Finally, we can calculate the average velocity using the formula:
Average velocity = Δx / Δt.
Average velocity = -37.5 / 3 = -12.5 meters per second.
Therefore, the average velocity during the time interval from t = 1s to t = 4s is -12.5 meters per second.
To find the average velocity during the time interval from t = 1s to t = 4s, we need to calculate the displacement and divide it by the time.
To calculate the displacement, we need to find the position at t = 1s and t = 4s and then subtract the initial position from the final position.
The position at t = 1s can be found by substituting t = 1 into the position equation:
x(1) = 13 + 11(1) - 1.5(1^2) = 13 + 11 - 1.5 = 22.5 meters
Similarly, we can find the position at t = 4s:
x(4) = 13 + 11(4) - 1.5(4^2) = 13 + 44 - 24 = 33 meters
Now, we can calculate the displacement:
Displacement = x(4) - x(1) = 33 - 22.5 = 10.5 meters
Next, we need to calculate the time interval:
Time interval = t(final) - t(initial) = 4s - 1s = 3 seconds
Finally, we can calculate the average velocity:
Average velocity = Displacement / Time interval = 10.5 meters / 3 seconds ≈ 3.5 meters per second
Therefore, the average velocity during the time interval from t = 1s to t = 4s is approximately 3.5 meters per second.